The Wolfram Language's symbolic character allows it to handle generalized functions or "distributions" as a direct extension of classical mathematical functions, and to represent integrals and integral transforms that cannot be expressed in terms of continuous functions.

DiracDelta — one-dimensional or multidimensional delta function

HeavisideTheta — Heaviside step function, for and for

DiracComb  ▪  HeavisidePi  ▪  HeavisideLambda

Integrate, D — integrals and derivatives of generalized functions

LaplaceTransform, FourierTransform — integral transforms

Convolve — convolve generalized functions

FunctionExpand — expand out generalized functions